A desk is being sold at 36% discount price. The sale price is $496.
What was its original price?

If the correlation coefficient r is -1.0, it means that there is a perfect negative linear relationship between X and Y.

a) As X scores increase, Y scores decrease in a perfectly consistent manner. The magnitude is strong.

b) If the correlation coefficient r is +0.32, it means that there is a positive linear relationship between X and Y, but it is a weak relationship. As X scores increase, Y scores tend to increase, but not in a perfectly consistent manner. The magnitude is weak.

c) If the correlation coefficient r is -0.10, it means that there is a weak negative linear relationship between X and Y. As X scores increase, Y scores tend to decrease, but not in a consistent manner. The magnitude is weak.

d) If the correlation coefficient r is -0.71, it means that there is a strong negative linear relationship between X and Y. As X scores increase, Y scores tend to decrease in a consistent manner. The magnitude is strong.

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Answer:

Divide the diameter by 2

Step-by-step explanation:

The rejection region for testing the hypothesis H₀: μ = 25 and H₁: μ ≠ 25, with a significance level of α = 0.05, is option D) Z < -1.96 or Z > 1.96.

In hypothesis testing, the rejection region is determined based on the significance level (α) and the nature of the alternative hypothesis. For a two-tailed test with α = 0.05, where H₀: μ = 25 and H₁: μ ≠ 25, the rejection region consists of extreme values in both tails of the distribution.

The critical values are determined by the z-score corresponding to a cumulative probability of (1 - α/2) on each tail. Since α = 0.05, the cumulative probability for each tail is (1 - 0.05/2) = 0.975. Looking up the z-score from the standard normal distribution table, we find that the critical z-value is approximately 1.96. Therefore, the rejection region is Z < -1.96 or Z > 1.96, which corresponds to option D) in the given choices.

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Answer:

hdhdb

Step-by-step explanation:

The solutions of the inequality \(2x^{2} + x - 6 = 0\) are 3/2, -2. This can be found by using the Quadratic Formula, which states that for any quadratic equation of the form \(ax^{2} +bx + c = 0\), the solutions are \(x = -b +/-\sqrt{b^{2} -4ac} /2a\).

Discriminant: b² - 4 a c = 1 - 4(2)(-6) = 1 + 48 = 49

Solution 1: x = \(-b + \sqrt{b^{2} -4ac} /2a\) = (-1 + √49)/(2×2) = (-1 +7)/4 = 6/4 = 3/2

Solution 2: x = \(-b-\sqrt{b^{2} -4ac} /2a\)= (-1 - √49)/(2×2) = -8/4 = -2

So, the two solutions are 3/2 and -2.

The equation can also be written as,

\(2x^{2} +4x -3x-6=0\)

\(2x(x+2) -3(x+2) = 0\)

\((2x-3)(x+2) = 0\)

x = 3/2, -2

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The first runner covers 30 yards in 4 seconds, a speed of 5 yards per second. The second runner covers a distance of 20 yards in 4 seconds but starts 10 yards ahead. Both runners have a speed of 5 yards per second.

The first runner maintains a constant speed of 5 yards per second and covers a distance of 30 yards in 4 seconds. The second runner also has a speed of 5 yards per second but starts 10 yards ahead. Therefore, the second runner covers a shorter distance of 20 yards in the same 4 seconds.

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By using the property of function, the result obtained is, When f(94) is divided by 1000, the remainder is 561

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Here the functional equation is given by

\(f(x) + f(x - 1) = x^2\)

Now,

\(f(x) + f(x - 1) = x^2\)

\(f(x) = x^2 - f(x - 1)\\f(94) = 94^2 - f(93) = 94^2 - 93^2 + f(92) =\\94^2 - 93^2 + 92^2 - f(91) = 94^2 - 93^2 + 92^2 -91^2+f(90)\)

\(94 + 93 + 92 + 91 + ..... +20^2 - f(19)\)

\(94 + 93 + 92 + ..... + 21 + 400 - 94\) [Since \(94 - 93 = 93 - 92 = .... = 1\)]

\(\frac{74}{2}(21 + 94) + 400 -94\)

\(37 \times 115 + 400 - 94\\4255 + 400 - 94\\4561\)

So f(94) = 4561

When 4561 is divided by 1000, the remainder is 561

So, when f(94) is divided by 1000, the remainder is 561

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Complete Question

The function f has the property that, for each real number x

\(f(x)+f(x-1) = x^2\)

If f(19)=94 what is the remainder when f(94) is divided by 1000?

The angles pairs that match each of the stated angle relationship are:

∠2 and ∠11 → alternate interior angles

∠9 and ∠16 → alternate exterior angles

∠1 and ∠10 → No relationship

∠3 and ∠5 → consecutive interior angles

∠7 and ∠15 → corresponding angles

Alternate Interior angles are angles that are found lying inside different parallel lines that are crossed by a transversal but on alternate sides along the transversal.

Alternate exterior angles are similar to alternate interior angles, but are angles that lie outside different parallel lines that are crossed by a transversal but on alternate sides along the transversal.

Angles that are referred to as corresponding angles are angles that are at relative corners on different parallel lines that are cut across by a transversal.

The angles named in the image above can be marched as follows:

∠2 and ∠11 → alternate interior angles

∠9 and ∠16 → alternate exterior angles

∠1 and ∠10 → No relationship

∠3 and ∠5 → consecutive interior angles

∠7 and ∠15 → corresponding angles

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Answer:

Average rate of change = -4

Step-by-step explanation:

Given:

f(x) = x² + 7x + 10

-8 ≤ x ≤ -3 or [-8, -3] in interval notation

Average rate of change of the function can be solved using the formula:

\(\mathrm{Average\:rate\:of\:change} = \dfrac{ f \left( b \right) -f \left( a \right) }{ b-a }\)

\(\mathrm{Average\:rate\:of\:change} = \dfrac{ f \left( -3 \right) -f \left( -8 \right) }{ -3 - (-8) }\)

\(\mathrm{Average\:rate\:of\:change} = \dfrac{ f \left( -3 \right) -f \left( -8 \right) }{ -3 + 8 }\)

\(\mathrm{Average\:rate\:of\:change} = \dfrac{ f \left( -3 \right) -f \left( -8 \right) }{ 5 }\)

Substitute x = -3 to the given function for f(-3) and x = -8 for f(-8)

\(\mathrm{Average\:rate\:of\:change} = \dfrac{ f \left( -3 \right) -f \left( -8 \right) }{ 5 }\)\(\mathrm{Average\:rate\:of\:change} = \dfrac{ { \left[( -3 \right) }^{ 2 } +7 \left( -3 \right) +10]- { \left[( -8 \right) }^{ 2 } +7 \left( -8 \right) +10] }{ 5 }\)

\(\mathrm{Average\:rate\:of\:change} = \dfrac{ [9-21+10]-[64-56+10] }{ 5 }\)

\(\mathrm{Average\:rate\:of\:change} = \dfrac{ [-2]-[18] }{ 5 }\)

\(\mathrm{Average\:rate\:of\:change} = \dfrac{ - 20 }{ 5 }\)

\(\mathrm{Average\:rate\:of\:change} = {-4 }\)

Answer: the initial points is 30.
and per pair of shoes is 15.

Step-by-step explanation:

The behavior of the graph of a polynomial function when the leading coefficient of an odd degree polynomial is greater than zero is the polynomial's final behavior will be "down" on the left and "up" on the right.

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1. Expressions that contain variables of various intensities, non-zero coefficients, positive exponents (of variables), and constants are known as polynomial functions. For instance, the polynomial in "b" of degree 2 is f(b) = 4b² - 6.

Given,

The behavior of the graph of a polynomial function when the leading coefficient of an odd degree polynomial is greater than zero is:

This odd-degree polynomial's end behavior will resemble that of a positive cubic because its leading coefficient is positive. As a result, the polynomial's final behavior will be "down" on the left and "up" on the right.

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Answer:

no but they can change in speed

Answer:

it depends

Step-by-step explanation

when there is a force its moving from some kind of energy ex: gravity

so when its faced with different energy it could change in position

Answer The answer is c.

Step-by-step explanation:

cause i said it was

The histograms typically are used to display continuous measures.

There are different types of charts: histogram, line chart, pie chart, and others.

The histogram is a type of chart used as a tool that provides a way to assess the distribution of data. From this type of chart, a set of data are previously tabulated and divided into classes. In the other words, the histogram is applied to summarize discrete or continuous measures, so it becomes more easily the understand the used data. There are many websites and software that allow the plot of this type of chart.

From the explanation, it is possible to identify the histograms typically are used to display continuous measures.

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The probability of having 7 boys in a family with 7 children is 1 out of 128, as there is only one favorable outcome out of 128 total possible outcomes.

To find the probability, we need to calculate n(E) and n(S).

In this case, event E represents the scenario where all 7 children are boys. The sample space S consists of all possible permutations of boys and girls for the 7 children, which is 2^7 = 128.

This is because each child has 2 possibilities (boy or girl), and we multiply these possibilities for all 7 children.

Since event E includes only one specific outcome (all boys), n(E) is equal to 1. Therefore, both n(E) and n(S) are 1 and 128, respectively. The probability of having 7 boys is given by n(E)/n(S) = 1/128.

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Answer:

Domain (-3, 4, 5)

Range (1, 2, 6)

Step-by-step explanation:

Domain is your x so all of the values that can go into a relation or function (which is your input) are called Domain. Domain is also all of the set of elements of ordered pair ( which is the x coordinates).

Range is your y so all the values that can go into a relation or function ( which is your output) are called Range. Range is also all the set of second elements of ordered pair ( which is the y coordinates).

So, basically you just look at all the number that come first so say you have

(1,2), (2,3), (3,4)

Your first numbers to each point are (1, 2, 3) which is your Domain

then look at the second number which are (2, 3, 4) which is your Range.

Hope this helps!

To determine the probability of at least three accounts being overdue in a random sample of five accounts, we can use the binomial probability formula. Given that 30% of the firm's accounts receivable are overdue, we can calculate the probability of each event and sum up the probabilities of having three, four, or five overdue accounts.

The probability of an account being overdue is given as 30%, which corresponds to a success in a binomial distribution. Let's denote p as the probability of success (overdue account), which is 0.30, and q as the probability of failure (account not overdue), which is 1 - p = 0.70.

To find the probability of at least three accounts being overdue, we need to sum up the probabilities of three, four, and five successes. We can calculate these probabilities using the binomial probability formula:

P(X = k) = (nCk) * p^k * q^(n-k)

where n is the sample size (5) and k is the number of successes (3, 4, or 5).

P(X ≥ 3) = P(X = 3) + P(X = 4) + P(X = 5)

          = (5C3) * (0.30)^3 * (0.70)^2 + (5C4) * (0.30)^4 * (0.70)^1 + (5C5) * (0.30)^5 * (0.70)^0

Calculating these probabilities will give us the desired probability of at least three accounts being overdue in the random sample.

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Answer:

y = - 3x

Step-by-step explanation:

an equation involving direct proportion has the form

y = kx ← k is the constant of proportion

the only equation in this form is

y = - 3x ( with k = - 3  )

Given :

Devon purchased a new car valued at $16,000 that depreciated continuously at a rate of 35%.

Its current value is $2,000.

To Find :

Age of car.

Solution :

Price of car after 1 year :

\(P_1=P_o(1-0.35)\)

Price of car after 2 year :

\(P_2=P_1(1-0.35)\\\\P_2=[P_o(1-0.35)](1-0.35)\\\\P_2=P_o(1-0.35)^2\)

So, price of car after n years.

\(P_n=P_o(1-0.35)^n\)

\(2000=16000(1-0.35)^n\\\\0.65^n=0.125\\\\n\times log(0.56)=log(0.125)\\\\n=\dfrac{log(0.125)}{log(0.56)}\\\\n=3.58\)

Therefore, age of car in nearest whole number is 4 years.

Hence, this is the required solution.

Sample space of randomly selecting a US state is 50, the probability that the US state begins with M is 4/25, and the probability that it doesn't begin with a vowel is 2/5.

a. What is the sample space?The sample space for randomly selecting one of the 50 US states is 50, i.e., the list of the 50 states.

b. What is the probability that it begins with M?The number of states that begin with M is 8. Therefore, the probability that the randomly selected US state begins with M is 8/50 or 4/25.

c. What is the probability that it doesn't begin with a vowel?There are 20 US states that don't begin with a vowel. Therefore, the probability that a randomly selected US state doesn't begin with a vowel is 20/50 or 2/5.

Randomly selecting a US state requires knowing the sample space, which in this case is 50. A sample space represents all possible outcomes of a random experiment. Therefore, the sample space for this problem represents the list of all 50 US states that can be randomly selected. The probability that a randomly selected US state begins with M can be calculated by dividing the number of states that begin with M by the total number of states. There are 8 US states that begin with M, hence, the probability of selecting a state that begins with M is 8/50 or 4/25. Finally, the probability that the randomly selected US state doesn't begin with a vowel is 20/50 or 2/5.

In conclusion, the sample space of selecting a US state randomly is 50, the probability that it begins with M is 4/25, and the probability that it doesn't begin with a vowel is 2/5.

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Answer:

The answer is A.

Step-by-step explanation:

4(0.5x+2.5y-0.7x-1.3y+4)

2x+10y+-2.8x+-5.2y+16

2x-2.8x+10y-5.2y+16

= -0.8x+4.8y+16

The standard deviation of the equivalent z-distribution is 0.25.

The standard deviation of the equivalent z-distribution can be calculated by dividing the standard deviation of the original distribution by the square root of the sample size.

In this case, since the strength of the component is normally distributed with a standard deviation of 2.5, we need to determine the standard deviation of the equivalent z-distribution.

To calculate this, we need to know the sample size. The z-distribution is used when we have a large sample size, typically considered to be 30 or greater.

Let's assume we have a sample size of 100.

The formula to calculate the standard deviation of the equivalent z-distribution is:

Standard deviation of the z-distribution = Standard deviation of the original distribution / √(sample size)

Substituting the values into the formula:

Standard deviation of the z-distribution = 2.5 / √(100)

Simplifying the expression:

Standard deviation of the z-distribution = 2.5 / 10

Standard deviation of the z-distribution = 0.25

Therefore, the standard deviation of the equivalent z-distribution is 0.25.

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The row of the input/output is incorrect is Row D.

Given equation: y = 2x - 3

For, row A:  

x = 3

y = 2x - 3

So,

y = 2(3) - 3

y = 3, which is correct

For row B:

x = 5

y = 2x - 3

So,

y = 2(5) - 3

y = 7, which is also correct.

For row C:

x = 7

y = 2x - 3

So,

y = 2(7) - 3

y = 11, which is also correct.

For, row D:

x = 10

y = 2x - 3

So, y = 2(10) - 3

y  = 17, which is incorrect.

Hence, the row of the input/output is incorrect is Row D.

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Answer:

point C

Step-by-step explanation:

all of the others go up by twos but point C went up to 8 instead of 6

Finding the square root of non-perfect square numbers typically results in an irrational number, which has a non-repeating and non-terminating decimal representation.

Finding the square root of a number involves determining the value that, when multiplied by itself, gives the original number. Here are a few methods to find the square root:

Prime Factorization: This method involves breaking down the number into its prime factors. Pair the factors in groups of two, and take one factor from each pair. Multiply these selected factors to find the square root. For example, to find the square root of 36, the prime factors are 2 * 2 * 3 * 3. Taking one factor from each pair (2 * 3), we get 6, which is the square root of 36.

Estimation: Approximate the square root using estimation techniques. Find the perfect square closest to the number you want to find the square root of and estimate the value in between. Refine the estimate using successive approximations if needed. For example, to find the square root of 23, we know that the square root of 25 is 5. Therefore, the square root of 23 will be slightly less than 5.

Using a Calculator: Most calculators have a square root function. Simply input the number and use the square root function to obtain the result.

It's important to note that finding the square root of non-perfect square numbers typically results in an irrational number, which has a non-repeating and non-terminating decimal representation.

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Answer:

4/3

Step-by-step explanation:

Slope is calculated by \(\frac{y1-y2}{x1-x2}\) so now you pul the points (10,2) and (19,14) into that.

\(\frac{14-2}{19-10}\) = \(\frac{12}{9}\)

12/9 can be simplified to be 4/3

Answer:

4/3

Step-by-step explanation:

Given,

Two points are (10,2) and (19,14)

To find the slope of the line passing through these points.

Answer:

x=7.9*tan(54°)=10.87